Abstract
The one-loop vertex in QED is calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, which is fully responsible for ensuring that the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in any covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the O(\ensuremath{\alpha}) vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes.
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